(* Title: HOL/Tools/typedef_package.ML
ID: $Id$
Author: Markus Wenzel, TU Muenchen
License: GPL (GNU GENERAL PUBLIC LICENSE)
Gordon/HOL-style type definitions.
*)
signature TYPEDEF_PACKAGE =
sig
val quiet_mode: bool ref
val add_typedecls: (bstring * string list * mixfix) list -> theory -> theory
val add_typedef_x: string -> bstring * string list * mixfix ->
string -> string list -> thm list -> tactic option -> theory -> theory
val add_typedef: bool -> string option -> bstring * string list * mixfix ->
string -> (bstring * bstring) option -> tactic -> theory -> theory *
{type_definition: thm, set_def: thm option, Rep: thm, Rep_inverse: thm,
Abs_inverse: thm, Rep_inject: thm, Abs_inject: thm, Rep_cases: thm, Abs_cases: thm,
Rep_induct: thm, Abs_induct: thm}
val add_typedef_i: bool -> string option -> bstring * string list * mixfix ->
term -> (bstring * bstring) option -> tactic -> theory -> theory *
{type_definition: thm, set_def: thm option, Rep: thm, Rep_inverse: thm,
Abs_inverse: thm, Rep_inject: thm, Abs_inject: thm, Rep_cases: thm, Abs_cases: thm,
Rep_induct: thm, Abs_induct: thm}
val typedef_proof: string * (bstring * string list * mixfix) * string * (string * string) option
-> bool -> theory -> ProofHistory.T
val typedef_proof_i: string * (bstring * string list * mixfix) * term * (string * string) option
-> bool -> theory -> ProofHistory.T
end;
structure TypedefPackage: TYPEDEF_PACKAGE =
struct
(** theory context references **)
val type_definitionN = "Typedef.type_definition";
val Rep = thm "type_definition.Rep";
val Rep_inverse = thm "type_definition.Rep_inverse";
val Abs_inverse = thm "type_definition.Abs_inverse";
val Rep_inject = thm "type_definition.Rep_inject";
val Abs_inject = thm "type_definition.Abs_inject";
val Rep_cases = thm "type_definition.Rep_cases";
val Abs_cases = thm "type_definition.Abs_cases";
val Rep_induct = thm "type_definition.Rep_induct";
val Abs_induct = thm "type_definition.Abs_induct";
(** type declarations **)
fun add_typedecls decls thy =
let
val full = Sign.full_name (Theory.sign_of thy);
fun arity_of (raw_name, args, mx) =
(full (Syntax.type_name raw_name mx), replicate (length args) HOLogic.typeS, HOLogic.typeS);
in
if can (Theory.assert_super HOL.thy) thy then
thy
|> PureThy.add_typedecls decls
|> Theory.add_arities_i (map arity_of decls)
else thy |> PureThy.add_typedecls decls
end;
(** type definitions **)
(* messages *)
val quiet_mode = ref false;
fun message s = if ! quiet_mode then () else writeln s;
(* prove_nonempty -- tactical version *) (*exception ERROR*)
fun prove_nonempty thy cset goal (witn1_tac, witn_names, witn_thms, witn2_tac) =
let
val is_def = Logic.is_equals o #prop o Thm.rep_thm;
val thms = PureThy.get_thmss thy witn_names @ witn_thms;
val tac =
witn1_tac THEN
TRY (rewrite_goals_tac (filter is_def thms)) THEN
TRY (REPEAT_FIRST (resolve_tac (filter_out is_def thms))) THEN
if_none witn2_tac (TRY (ALLGOALS (CLASET' blast_tac)));
in
message ("Proving non-emptiness of set " ^ quote (string_of_cterm cset) ^ " ...");
Tactic.prove (Theory.sign_of thy) [] [] goal (K tac)
end handle ERROR => error ("Failed to prove non-emptiness of " ^ quote (string_of_cterm cset));
(* prepare_typedef *)
fun read_term sg used s =
#1 (Thm.read_def_cterm (sg, K None, K None) used true (s, HOLogic.typeT));
fun cert_term sg _ t = Thm.cterm_of sg t handle TERM (msg, _) => error msg;
fun err_in_typedef name =
error ("The error(s) above occurred in typedef " ^ quote name);
fun prepare_typedef prep_term def name (t, vs, mx) raw_set opt_morphs thy =
let
val _ = Theory.requires thy "Typedef" "typedefs";
val sign = Theory.sign_of thy;
val full = Sign.full_name sign;
(*rhs*)
val full_name = full name;
val cset = prep_term sign vs raw_set;
val {T = setT, t = set, ...} = Thm.rep_cterm cset;
val rhs_tfrees = term_tfrees set;
val oldT = HOLogic.dest_setT setT handle TYPE _ =>
error ("Not a set type: " ^ quote (Sign.string_of_typ sign setT));
fun mk_nonempty A =
HOLogic.mk_Trueprop (HOLogic.mk_exists ("x", oldT, HOLogic.mk_mem (Free ("x", oldT), A)));
val goal = mk_nonempty set;
val vname = take_suffix Symbol.is_digit (Symbol.explode name)
|> apfst implode |> apsnd (#1 o Term.read_int);
val goal_pat = mk_nonempty (Var (vname, setT));
(*lhs*)
val lhs_tfrees = map (fn v => (v, if_none (assoc (rhs_tfrees, v)) HOLogic.typeS)) vs;
val tname = Syntax.type_name t mx;
val full_tname = full tname;
val newT = Type (full_tname, map TFree lhs_tfrees);
val (Rep_name, Abs_name) = if_none opt_morphs ("Rep_" ^ name, "Abs_" ^ name);
val setC = Const (full_name, setT);
val RepC = Const (full Rep_name, newT --> oldT);
val AbsC = Const (full Abs_name, oldT --> newT);
val x_new = Free ("x", newT);
val y_old = Free ("y", oldT);
val set' = if def then setC else set;
val typedef_name = "type_definition_" ^ name;
val typedefC =
Const (type_definitionN, (newT --> oldT) --> (oldT --> newT) --> setT --> HOLogic.boolT);
val typedef_prop =
Logic.mk_implies (goal, HOLogic.mk_Trueprop (typedefC $ RepC $ AbsC $ set'));
fun typedef_result (theory, nonempty) =
theory
|> add_typedecls [(t, vs, mx)]
|> Theory.add_consts_i
((if def then [(name, setT, NoSyn)] else []) @
[(Rep_name, newT --> oldT, NoSyn),
(Abs_name, oldT --> newT, NoSyn)])
|> (if def then (apsnd (Some o hd) oo (PureThy.add_defs_i false o map Thm.no_attributes))
[Logic.mk_defpair (setC, set)]
else rpair None)
|>> PureThy.add_axioms_i [((typedef_name, typedef_prop),
[apsnd (fn cond_axm => Drule.standard (nonempty RS cond_axm))])]
|> (fn ((theory', [type_definition]), set_def) =>
let
fun make th = Drule.standard (th OF [type_definition]);
val (theory'', [Rep, Rep_inverse, Abs_inverse, Rep_inject, Abs_inject,
Rep_cases, Abs_cases, Rep_induct, Abs_induct]) =
theory'
|> Theory.add_path name
|> PureThy.add_thms
([((Rep_name, make Rep), []),
((Rep_name ^ "_inverse", make Rep_inverse), []),
((Abs_name ^ "_inverse", make Abs_inverse), []),
((Rep_name ^ "_inject", make Rep_inject), []),
((Abs_name ^ "_inject", make Abs_inject), []),
((Rep_name ^ "_cases", make Rep_cases),
[RuleCases.case_names [Rep_name], InductAttrib.cases_set_global full_name]),
((Abs_name ^ "_cases", make Abs_cases),
[RuleCases.case_names [Abs_name], InductAttrib.cases_type_global full_tname]),
((Rep_name ^ "_induct", make Rep_induct),
[RuleCases.case_names [Rep_name], InductAttrib.induct_set_global full_name]),
((Abs_name ^ "_induct", make Abs_induct),
[RuleCases.case_names [Abs_name], InductAttrib.induct_type_global full_tname])])
|>> Theory.parent_path;
val result = {type_definition = type_definition, set_def = set_def,
Rep = Rep, Rep_inverse = Rep_inverse, Abs_inverse = Abs_inverse,
Rep_inject = Rep_inject, Abs_inject = Abs_inject, Rep_cases = Rep_cases,
Abs_cases = Abs_cases, Rep_induct = Rep_induct, Abs_induct = Abs_induct};
in ((theory'', type_definition), result) end);
(* errors *)
fun show_names pairs = commas_quote (map fst pairs);
val illegal_vars =
if null (term_vars set) andalso null (term_tvars set) then []
else ["Illegal schematic variable(s) on rhs"];
val dup_lhs_tfrees =
(case duplicates lhs_tfrees of [] => []
| dups => ["Duplicate type variables on lhs: " ^ show_names dups]);
val extra_rhs_tfrees =
(case gen_rems (op =) (rhs_tfrees, lhs_tfrees) of [] => []
| extras => ["Extra type variables on rhs: " ^ show_names extras]);
val illegal_frees =
(case term_frees set of [] => []
| xs => ["Illegal variables on rhs: " ^ show_names (map dest_Free xs)]);
val errs = illegal_vars @ dup_lhs_tfrees @ extra_rhs_tfrees @ illegal_frees;
val _ = if null errs then () else error (cat_lines errs);
(*test theory errors now!*)
val test_thy = Theory.copy thy;
val _ = (test_thy,
setmp quick_and_dirty true (SkipProof.make_thm test_thy) goal) |> typedef_result;
in (cset, goal, goal_pat, typedef_result) end
handle ERROR => err_in_typedef name;
(* add_typedef interfaces *)
fun gen_typedef prep_term def name typ set opt_morphs tac1 names thms tac2 thy =
let
val (cset, goal, _, typedef_result) =
prepare_typedef prep_term def name typ set opt_morphs thy;
val non_empty = prove_nonempty thy cset goal (tac1, names, thms, tac2);
val ((thy', _), result) = (thy, non_empty) |> typedef_result;
in (thy', result) end;
fun sane_typedef prep_term def opt_name typ set opt_morphs tac =
gen_typedef prep_term def
(if_none opt_name (#1 typ)) typ set opt_morphs all_tac [] [] (Some tac);
fun add_typedef_x name typ set names thms tac =
#1 o gen_typedef read_term true name typ set None (Tactic.rtac exI 1) names thms tac;
val add_typedef = sane_typedef read_term;
val add_typedef_i = sane_typedef cert_term;
(* typedef_proof interface *)
fun gen_typedef_proof prep_term (name, typ, set, opt_morphs) int thy =
let
val (_, goal, goal_pat, att_result) =
prepare_typedef prep_term true name typ set opt_morphs thy;
val att = #1 o att_result;
in thy |> IsarThy.theorem_i Drule.internalK (("", [att]), (goal, ([goal_pat], []))) int end;
val typedef_proof = gen_typedef_proof read_term;
val typedef_proof_i = gen_typedef_proof cert_term;
(** outer syntax **)
local structure P = OuterParse and K = OuterSyntax.Keyword in
val typedeclP =
OuterSyntax.command "typedecl" "type declaration (HOL)" K.thy_decl
(P.type_args -- P.name -- P.opt_infix >> (fn ((vs, t), mx) =>
Toplevel.theory (add_typedecls [(t, vs, mx)])));
val typedef_proof_decl =
Scan.option (P.$$$ "(" |-- P.name --| P.$$$ ")") --
(P.type_args -- P.name) -- P.opt_infix -- (P.$$$ "=" |-- P.term) --
Scan.option (P.$$$ "morphisms" |-- P.!!! (P.name -- P.name));
fun mk_typedef_proof ((((opt_name, (vs, t)), mx), A), morphs) =
typedef_proof (if_none opt_name (Syntax.type_name t mx), (t, vs, mx), A, morphs);
val typedefP =
OuterSyntax.command "typedef" "HOL type definition (requires non-emptiness proof)" K.thy_goal
(typedef_proof_decl >> (Toplevel.print oo (Toplevel.theory_to_proof o mk_typedef_proof)));
val _ = OuterSyntax.add_keywords ["morphisms"];
val _ = OuterSyntax.add_parsers [typedeclP, typedefP];
end;
end;